Barrel rolls are quite easy with a trainer. Dive for speed and then start a straight climb of 45 degrees. Before the airplane slows down, feed in aileron and rudder and keep them there until the airplane rolls around back to upright.

Barrel rolls are a positive G maneuver so you are not feeding in elevator. Just leave it alone as you do a barrel roll.
For learning axial and barrel rolls, make sure you start on a good "up line". You will get there by just practicing more.